Solution to the forward and backward stochastic difference equations with asymmetric information and application

Abstract

This paper is concerned with a kind of infinite horizon forward and backward stochastic difference equations (FBSDEs) with asymmetric information. The asymmetric information means that there exists two kinds of conditional expectations with respect to two different filtrations caused by the additive noise and the measurement packet dropout. The main contribution is to present the analytical solutions of the FBSDEs with asymmetric information. The key technique is to establish non-homogenous relationship between the backward stochastic process and the estimation of the forward stochastic process. As applications, we obtain the optimal solution to the infinite horizon stochastic linear quadratic (LQ) optimal control with asymmetric information.